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Scott Armstrong math 54 quiz 2

Scott Armstrong math 54 quiz 2 - v Nain‘i‘...

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Unformatted text preview: v Nain‘i‘ So\o“\i®\r\g ' ' Quiz 2 . - Math 54 — Summer 2008 ’ i. July 2, 2008 1. Determine whether the linear transformation Whose standard matrix is 1 1 2 —3 A = —2 ——3 —2 - 5 , 3 —1 4 0 is onto, and whether it is one— -to- -one. 33 TW \vx c,\01$$ LA iS ofl'3f0 ,. \a ‘2 (A 193 v Q A a La wms o SQM \ L9 (5 oN-‘i‘o— bv{ L: bo\uwms c o.&\w.ur\13 W Do Nw 095 “\W—A Q'Rf‘Rx—a R» , "ERN‘; '5) R3 .' ‘ ‘ 1.1 l —3 o -, 1 «1 o O -10 Y5 1 1 1 -3 g “L 37" ”‘1‘ Tke ca.\w\.91}m S‘on35 431431 NW3 W has 0‘ Pwo'i SD "HQ Odom“) 1:? A SWYHfRs‘ 30 L9 15 oMo' \“\ 0A9; shows Jewfi +N Column; ' 0‘2 91 we mm mm, am '14». w Ooh-1M“ was no pNO‘i 50 L9 IS 2. Find the standard matrix for the linear transformation from R2 to R2, which acts on an “5’? MW input vector x by first rotating it counterclockwise by 7r/ 4 and then reflecting it through AM they-axis. W 15811:“ by. This “\‘Lz 31M matrix 3%; Cos? gin: “It. ‘57:. “36M- “W WQMCOA {5 I 3k]; C0517: 6."; a”. [_\ 0'] [ch (a, «Shaw is givenbjz 0_ ‘ Gil <5." .0...‘\ ‘ . ah. Gin. ...
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